Answer:
The value is 
Explanation:
From the question we are told that
The length of the bottom of the barge below the water line when loaded is 
The length of the bottom of the barge below the water line when empty is 
Generally the difference in pressure is mathematically represented as
Here 
is the density of water with value 
=>
Will reduce 4 times.
So called LUG (Law of Universal gravitation).
when we placed in the container of real depth assuming = d
if the container filled with liquid A then its apparent depth d' = 7cm
so the refractive index nA = real depth / apparent depth
= d/7cm = 0.1428d
if the container filled with liquid B then its apparent depth d' = 6cm
so the refractive index nB = real depth / apparent depth
= d/6cm = 0.166d
if the container filled with liquid C then its apparent depth d' = 5cm
so the refractive index nC = real depth / apparent depth
= d/5cm = 0.2d
Since the refractive index is inversely proportional to the apparent depth
then the refractive indices are nC > nB > nA
